EXACT ANALYTIC FORMULA FOR THE CORRELATION TIME OF A SINGLE-DOMAIN FERROMAGNETIC PARTICLE

Exact solutions for the longitudinal relaxation time T(parallel-to) an d the complex susceptibility chi(parallel-to)(omega) of a thermally ag itated single-domain ferromagnetic particle are presented for the simp le uniaxial potential of the crystalline anisotropy considered by Brow n [Phys. Rev. 130, 1677 (1963)]. This is accomplished by expanding the spatial part of the distribution function of magnetic-moment orientat ions on the unit sphere in the Fokker-Planck equation in Legendre poly nomials. This leads to the three-term recurrence relation for the Lapl ace transform of the decay functions. The recurrence relation may be s olved exactly in terms of continued fractions. The zero-frequency limi t of the solution yields an analytic formula for T(parallel-to) as a s eries of confluent hypergeometric (Kummer) functions which is easily t abulated for all potential-barrier heights. The asymptotic formula for T(parallel-to) of Brown is recovered in the limit of high barriers. O n conversion of the exact solution for T(parallel-to) to integral form , it is shown using the method of steepest descents that an asymptotic correction to Brown's high-barrier result is necessary. The inadequac y of the effective-eigenvalue method as applied to the calculation of T(parallel-to) is discussed.